
Problem
Last Sunday, the average temperature was 
\[8\%\] higher than the average temperature two Sundays ago. The average temperature two Sundays ago was 
\[T\] degrees Celsius.
Which of the following expressions could represent the average temperature last Sunday?
Choose 2 answers:
Choose 2 answers:
(Choice A)   
 
\[\left(1+\dfrac{8}{100}\right)T\]
A
 
\[\left(1+\dfrac{8}{100}\right)T\]
(Choice B)   
\[1.08T\]
B
\[1.08T\]
(Choice C)   
\[1.8T\]
C
\[1.8T\]
(Choice D)   
\[T+0.08\]
D
\[T+0.08\]
(Choice E)   
\[T+8\]
E
\[T+8\]


We are told that the average temperature last Sunday was 8% higher than the average temperature two Sundays ago, which was \( T \) degrees Celsius.

To find the temperature last Sunday, we can increase \( T \) by 8%. Here's how:

1. **Convert 8% to a decimal**:  
   \[
   8\% = \dfrac{8}{100} = 0.08
   \]

2. **Increase \( T \) by 8%**:  
   The new temperature can be found by adding 8% of \( T \) to \( T \). Mathematically, this is:  
   \[
   T + 0.08T = (1 + 0.08)T = 1.08T
   \]

So, the temperature last Sunday can be represented by either of the following expressions:
- \( \left(1 + \dfrac{8}{100}\right)T \) (which simplifies to \( 1.08T \))  
- \( 1.08T \)

### Therefore, the correct choices are:
- **Choice A**: \( \left(1 + \dfrac{8}{100}\right)T \)
- **Choice B**: \( 1.08T \)

### Explanation of the incorrect options:
- **Choice C**: \( 1.8T \) is incorrect because it represents an 80% increase, not 8%.
- **Choice D**: \( T + 0.08 \) is incorrect because adding 0.08 is not the same as adding 8% of \( T \).
- **Choice E**: \( T + 8 \) is incorrect because it adds 8 degrees, not 8%.

Would you like further details on this? Here are some related questions to explore:

1. What happens if the temperature increase is 12% instead of 8%?
2. How do you calculate percentage increases in general?
3. What is the effect of an 8% decrease on \( T \)?
4. Can percentage increases and decreases be combined in a single expression?
5. How can compound percentage changes be calculated over multiple periods?

**Tip:** When dealing with percentages, always convert them to decimals to make calculations easier.

Last Sunday, the average temperature was 8% higher than the average temperature two Sundays ago. The average temperature two Sundays ago was T degrees Celsius. Which of the following expressions could represent the average temperature last Sunday? Choose 2 answers: (Choice A) (1 + 8/100)T, (Choice B) 1.08T, (Choice C) 1.8T, (Choice D) T + 0.08, (Choice E) T + 8

Learn how to calculate the percentage increase in temperature, specifically an 8% increase from a previous value. This problem demonstrates how to apply algebraic concepts and percentage formulas. Suitable for students in Grades 6-8.

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